this is like a theory and practice situation. in theory this is conflict of interest issue possibly undermines objectivity and so on. in practice Nvidia thrives and the man is a substantial reason of this. removing him will be plain stupid from the point of view of the company's performance.

Company success has nothing to do with the conflicts of interest above though.

But keeping him potentially exposes them legally. If she ever accused him of using his authority to coerce her into said relationship (purely hypothetical), the board is now complicit in covering up legit criminal behavior. This is why conflict of interest policy exists.

fair point but is it solvable by other means? like the board "to conduct investigation", discuss with this woman if she has been coerced and if she claims she is not — avoid firing him?

Why should we assume corporate codes are morally just though? I do not. In fact I would argue this is evidence that company codes are in a general sense draconian and/or disconnected from social reality under capitalism, etc.

Many (most?) companies have specific policies against romantic relationships in the office, especially with subordinates.

It isn't necessarily about morality if there are rules in place that all employees, c-suite or otherwise, are expected to follow.

I don't know Nvidia internal policy, but assuming their HR policies include such a stipulation it shouldn't be treated as a "rules for thee, not me for" situation.

He's the CEO. It's _his_ code of conduct.

Sure, but he answers to the board and the shareholders. Everybody's got a boss.